It means get a letter from a professor or research advisor or Dean of Students if you are already in med school. Do not get letter from your high school wrestling coach, your boss at the summer parks and rec job or your minister. A letter from your parents, even if they are military, looks weird as well. And yes the earlier you apply the better because these scholarships are given out first come first serve. So apply with the first acceptance letter you get even if you would rather attend Iowa instead of the Waterloo School of Sacred Manipulation, you can change the school later in the process.